Abstract: We examine the role of session key construction in provably-
secure key establishment protocols. We revisit an ID-based key establishment protocol due to Chen & Kudla (2003) and an ID-based protocol 2P-IDAKA due to McCullagh & Barreto (2005). Both protocols carry proofs of security in a weaker variant of the Bellare & Rogaway (1993) model where the adversary is not allowed to make any Reveal query. We advocate the importance of such a (Reveal) query as it captures the known-key security requirement. We then demonstrate that a small change to the way that session keys are constructed in both protocols results in these protocols being secure without restricting the adversary from asking the Reveal queries in most situations. We point out some errors in the existing proof for protocol 2P-IDAKA, and provide proof sketches for the improved Chen & Kudla's protocol. We conclude with a brief discussion on ways to construct session keys in key establishment protocols.